1 //===- ScalarEvolution.cpp - Scalar Evolution Analysis ----------*- C++ -*-===//
3 // The LLVM Compiler Infrastructure
5 // This file was developed by the LLVM research group and is distributed under
6 // the University of Illinois Open Source License. See LICENSE.TXT for details.
8 //===----------------------------------------------------------------------===//
10 // This file contains the implementation of the scalar evolution analysis
11 // engine, which is used primarily to analyze expressions involving induction
12 // variables in loops.
14 // There are several aspects to this library. First is the representation of
15 // scalar expressions, which are represented as subclasses of the SCEV class.
16 // These classes are used to represent certain types of subexpressions that we
17 // can handle. These classes are reference counted, managed by the SCEVHandle
18 // class. We only create one SCEV of a particular shape, so pointer-comparisons
19 // for equality are legal.
21 // One important aspect of the SCEV objects is that they are never cyclic, even
22 // if there is a cycle in the dataflow for an expression (ie, a PHI node). If
23 // the PHI node is one of the idioms that we can represent (e.g., a polynomial
24 // recurrence) then we represent it directly as a recurrence node, otherwise we
25 // represent it as a SCEVUnknown node.
27 // In addition to being able to represent expressions of various types, we also
28 // have folders that are used to build the *canonical* representation for a
29 // particular expression. These folders are capable of using a variety of
30 // rewrite rules to simplify the expressions.
32 // Once the folders are defined, we can implement the more interesting
33 // higher-level code, such as the code that recognizes PHI nodes of various
34 // types, computes the execution count of a loop, etc.
36 // TODO: We should use these routines and value representations to implement
37 // dependence analysis!
39 //===----------------------------------------------------------------------===//
41 // There are several good references for the techniques used in this analysis.
43 // Chains of recurrences -- a method to expedite the evaluation
44 // of closed-form functions
45 // Olaf Bachmann, Paul S. Wang, Eugene V. Zima
47 // On computational properties of chains of recurrences
50 // Symbolic Evaluation of Chains of Recurrences for Loop Optimization
51 // Robert A. van Engelen
53 // Efficient Symbolic Analysis for Optimizing Compilers
54 // Robert A. van Engelen
56 // Using the chains of recurrences algebra for data dependence testing and
57 // induction variable substitution
58 // MS Thesis, Johnie Birch
60 //===----------------------------------------------------------------------===//
62 #include "llvm/Analysis/ScalarEvolutionExpressions.h"
63 #include "llvm/Constants.h"
64 #include "llvm/DerivedTypes.h"
65 #include "llvm/GlobalVariable.h"
66 #include "llvm/Instructions.h"
67 #include "llvm/Analysis/ConstantFolding.h"
68 #include "llvm/Analysis/LoopInfo.h"
69 #include "llvm/Assembly/Writer.h"
70 #include "llvm/Transforms/Scalar.h"
71 #include "llvm/Support/CFG.h"
72 #include "llvm/Support/CommandLine.h"
73 #include "llvm/Support/Compiler.h"
74 #include "llvm/Support/ConstantRange.h"
75 #include "llvm/Support/InstIterator.h"
76 #include "llvm/Support/ManagedStatic.h"
77 #include "llvm/ADT/Statistic.h"
84 RegisterPass<ScalarEvolution>
85 R("scalar-evolution", "Scalar Evolution Analysis");
88 NumBruteForceEvaluations("scalar-evolution",
89 "Number of brute force evaluations needed to "
90 "calculate high-order polynomial exit values");
92 NumArrayLenItCounts("scalar-evolution",
93 "Number of trip counts computed with array length");
95 NumTripCountsComputed("scalar-evolution",
96 "Number of loops with predictable loop counts");
98 NumTripCountsNotComputed("scalar-evolution",
99 "Number of loops without predictable loop counts");
101 NumBruteForceTripCountsComputed("scalar-evolution",
102 "Number of loops with trip counts computed by force");
105 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
106 cl::desc("Maximum number of iterations SCEV will "
107 "symbolically execute a constant derived loop"),
111 //===----------------------------------------------------------------------===//
112 // SCEV class definitions
113 //===----------------------------------------------------------------------===//
115 //===----------------------------------------------------------------------===//
116 // Implementation of the SCEV class.
119 void SCEV::dump() const {
123 /// getValueRange - Return the tightest constant bounds that this value is
124 /// known to have. This method is only valid on integer SCEV objects.
125 ConstantRange SCEV::getValueRange() const {
126 const Type *Ty = getType();
127 assert(Ty->isInteger() && "Can't get range for a non-integer SCEV!");
128 Ty = Ty->getUnsignedVersion();
129 // Default to a full range if no better information is available.
130 return ConstantRange(getType());
134 SCEVCouldNotCompute::SCEVCouldNotCompute() : SCEV(scCouldNotCompute) {}
136 bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const {
137 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
141 const Type *SCEVCouldNotCompute::getType() const {
142 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
146 bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const {
147 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
151 SCEVHandle SCEVCouldNotCompute::
152 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
153 const SCEVHandle &Conc) const {
157 void SCEVCouldNotCompute::print(std::ostream &OS) const {
158 OS << "***COULDNOTCOMPUTE***";
161 bool SCEVCouldNotCompute::classof(const SCEV *S) {
162 return S->getSCEVType() == scCouldNotCompute;
166 // SCEVConstants - Only allow the creation of one SCEVConstant for any
167 // particular value. Don't use a SCEVHandle here, or else the object will
169 static ManagedStatic<std::map<ConstantInt*, SCEVConstant*> > SCEVConstants;
172 SCEVConstant::~SCEVConstant() {
173 SCEVConstants->erase(V);
176 SCEVHandle SCEVConstant::get(ConstantInt *V) {
177 // Make sure that SCEVConstant instances are all unsigned.
178 if (V->getType()->isSigned()) {
179 const Type *NewTy = V->getType()->getUnsignedVersion();
180 V = cast<ConstantInt>(ConstantExpr::getCast(V, NewTy));
183 SCEVConstant *&R = (*SCEVConstants)[V];
184 if (R == 0) R = new SCEVConstant(V);
188 ConstantRange SCEVConstant::getValueRange() const {
189 return ConstantRange(V);
192 const Type *SCEVConstant::getType() const { return V->getType(); }
194 void SCEVConstant::print(std::ostream &OS) const {
195 WriteAsOperand(OS, V, false);
198 // SCEVTruncates - Only allow the creation of one SCEVTruncateExpr for any
199 // particular input. Don't use a SCEVHandle here, or else the object will
201 static ManagedStatic<std::map<std::pair<SCEV*, const Type*>,
202 SCEVTruncateExpr*> > SCEVTruncates;
204 SCEVTruncateExpr::SCEVTruncateExpr(const SCEVHandle &op, const Type *ty)
205 : SCEV(scTruncate), Op(op), Ty(ty) {
206 assert(Op->getType()->isInteger() && Ty->isInteger() &&
208 "Cannot truncate non-integer value!");
209 assert(Op->getType()->getPrimitiveSize() > Ty->getPrimitiveSize() &&
210 "This is not a truncating conversion!");
213 SCEVTruncateExpr::~SCEVTruncateExpr() {
214 SCEVTruncates->erase(std::make_pair(Op, Ty));
217 ConstantRange SCEVTruncateExpr::getValueRange() const {
218 return getOperand()->getValueRange().truncate(getType());
221 void SCEVTruncateExpr::print(std::ostream &OS) const {
222 OS << "(truncate " << *Op << " to " << *Ty << ")";
225 // SCEVZeroExtends - Only allow the creation of one SCEVZeroExtendExpr for any
226 // particular input. Don't use a SCEVHandle here, or else the object will never
228 static ManagedStatic<std::map<std::pair<SCEV*, const Type*>,
229 SCEVZeroExtendExpr*> > SCEVZeroExtends;
231 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const SCEVHandle &op, const Type *ty)
232 : SCEV(scTruncate), Op(op), Ty(ty) {
233 assert(Op->getType()->isInteger() && Ty->isInteger() &&
235 "Cannot zero extend non-integer value!");
236 assert(Op->getType()->getPrimitiveSize() < Ty->getPrimitiveSize() &&
237 "This is not an extending conversion!");
240 SCEVZeroExtendExpr::~SCEVZeroExtendExpr() {
241 SCEVZeroExtends->erase(std::make_pair(Op, Ty));
244 ConstantRange SCEVZeroExtendExpr::getValueRange() const {
245 return getOperand()->getValueRange().zeroExtend(getType());
248 void SCEVZeroExtendExpr::print(std::ostream &OS) const {
249 OS << "(zeroextend " << *Op << " to " << *Ty << ")";
252 // SCEVCommExprs - Only allow the creation of one SCEVCommutativeExpr for any
253 // particular input. Don't use a SCEVHandle here, or else the object will never
255 static ManagedStatic<std::map<std::pair<unsigned, std::vector<SCEV*> >,
256 SCEVCommutativeExpr*> > SCEVCommExprs;
258 SCEVCommutativeExpr::~SCEVCommutativeExpr() {
259 SCEVCommExprs->erase(std::make_pair(getSCEVType(),
260 std::vector<SCEV*>(Operands.begin(),
264 void SCEVCommutativeExpr::print(std::ostream &OS) const {
265 assert(Operands.size() > 1 && "This plus expr shouldn't exist!");
266 const char *OpStr = getOperationStr();
267 OS << "(" << *Operands[0];
268 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
269 OS << OpStr << *Operands[i];
273 SCEVHandle SCEVCommutativeExpr::
274 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
275 const SCEVHandle &Conc) const {
276 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
277 SCEVHandle H = getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc);
278 if (H != getOperand(i)) {
279 std::vector<SCEVHandle> NewOps;
280 NewOps.reserve(getNumOperands());
281 for (unsigned j = 0; j != i; ++j)
282 NewOps.push_back(getOperand(j));
284 for (++i; i != e; ++i)
285 NewOps.push_back(getOperand(i)->
286 replaceSymbolicValuesWithConcrete(Sym, Conc));
288 if (isa<SCEVAddExpr>(this))
289 return SCEVAddExpr::get(NewOps);
290 else if (isa<SCEVMulExpr>(this))
291 return SCEVMulExpr::get(NewOps);
293 assert(0 && "Unknown commutative expr!");
300 // SCEVSDivs - Only allow the creation of one SCEVSDivExpr for any particular
301 // input. Don't use a SCEVHandle here, or else the object will never be
303 static ManagedStatic<std::map<std::pair<SCEV*, SCEV*>,
304 SCEVSDivExpr*> > SCEVSDivs;
306 SCEVSDivExpr::~SCEVSDivExpr() {
307 SCEVSDivs->erase(std::make_pair(LHS, RHS));
310 void SCEVSDivExpr::print(std::ostream &OS) const {
311 OS << "(" << *LHS << " /s " << *RHS << ")";
314 const Type *SCEVSDivExpr::getType() const {
315 const Type *Ty = LHS->getType();
316 if (Ty->isUnsigned()) Ty = Ty->getSignedVersion();
320 // SCEVAddRecExprs - Only allow the creation of one SCEVAddRecExpr for any
321 // particular input. Don't use a SCEVHandle here, or else the object will never
323 static ManagedStatic<std::map<std::pair<const Loop *, std::vector<SCEV*> >,
324 SCEVAddRecExpr*> > SCEVAddRecExprs;
326 SCEVAddRecExpr::~SCEVAddRecExpr() {
327 SCEVAddRecExprs->erase(std::make_pair(L,
328 std::vector<SCEV*>(Operands.begin(),
332 SCEVHandle SCEVAddRecExpr::
333 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
334 const SCEVHandle &Conc) const {
335 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
336 SCEVHandle H = getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc);
337 if (H != getOperand(i)) {
338 std::vector<SCEVHandle> NewOps;
339 NewOps.reserve(getNumOperands());
340 for (unsigned j = 0; j != i; ++j)
341 NewOps.push_back(getOperand(j));
343 for (++i; i != e; ++i)
344 NewOps.push_back(getOperand(i)->
345 replaceSymbolicValuesWithConcrete(Sym, Conc));
347 return get(NewOps, L);
354 bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const {
355 // This recurrence is invariant w.r.t to QueryLoop iff QueryLoop doesn't
356 // contain L and if the start is invariant.
357 return !QueryLoop->contains(L->getHeader()) &&
358 getOperand(0)->isLoopInvariant(QueryLoop);
362 void SCEVAddRecExpr::print(std::ostream &OS) const {
363 OS << "{" << *Operands[0];
364 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
365 OS << ",+," << *Operands[i];
366 OS << "}<" << L->getHeader()->getName() + ">";
369 // SCEVUnknowns - Only allow the creation of one SCEVUnknown for any particular
370 // value. Don't use a SCEVHandle here, or else the object will never be
372 static ManagedStatic<std::map<Value*, SCEVUnknown*> > SCEVUnknowns;
374 SCEVUnknown::~SCEVUnknown() { SCEVUnknowns->erase(V); }
376 bool SCEVUnknown::isLoopInvariant(const Loop *L) const {
377 // All non-instruction values are loop invariant. All instructions are loop
378 // invariant if they are not contained in the specified loop.
379 if (Instruction *I = dyn_cast<Instruction>(V))
380 return !L->contains(I->getParent());
384 const Type *SCEVUnknown::getType() const {
388 void SCEVUnknown::print(std::ostream &OS) const {
389 WriteAsOperand(OS, V, false);
392 //===----------------------------------------------------------------------===//
394 //===----------------------------------------------------------------------===//
397 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
398 /// than the complexity of the RHS. This comparator is used to canonicalize
400 struct VISIBILITY_HIDDEN SCEVComplexityCompare {
401 bool operator()(SCEV *LHS, SCEV *RHS) {
402 return LHS->getSCEVType() < RHS->getSCEVType();
407 /// GroupByComplexity - Given a list of SCEV objects, order them by their
408 /// complexity, and group objects of the same complexity together by value.
409 /// When this routine is finished, we know that any duplicates in the vector are
410 /// consecutive and that complexity is monotonically increasing.
412 /// Note that we go take special precautions to ensure that we get determinstic
413 /// results from this routine. In other words, we don't want the results of
414 /// this to depend on where the addresses of various SCEV objects happened to
417 static void GroupByComplexity(std::vector<SCEVHandle> &Ops) {
418 if (Ops.size() < 2) return; // Noop
419 if (Ops.size() == 2) {
420 // This is the common case, which also happens to be trivially simple.
422 if (Ops[0]->getSCEVType() > Ops[1]->getSCEVType())
423 std::swap(Ops[0], Ops[1]);
427 // Do the rough sort by complexity.
428 std::sort(Ops.begin(), Ops.end(), SCEVComplexityCompare());
430 // Now that we are sorted by complexity, group elements of the same
431 // complexity. Note that this is, at worst, N^2, but the vector is likely to
432 // be extremely short in practice. Note that we take this approach because we
433 // do not want to depend on the addresses of the objects we are grouping.
434 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
436 unsigned Complexity = S->getSCEVType();
438 // If there are any objects of the same complexity and same value as this
440 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
441 if (Ops[j] == S) { // Found a duplicate.
442 // Move it to immediately after i'th element.
443 std::swap(Ops[i+1], Ops[j]);
444 ++i; // no need to rescan it.
445 if (i == e-2) return; // Done!
453 //===----------------------------------------------------------------------===//
454 // Simple SCEV method implementations
455 //===----------------------------------------------------------------------===//
457 /// getIntegerSCEV - Given an integer or FP type, create a constant for the
458 /// specified signed integer value and return a SCEV for the constant.
459 SCEVHandle SCEVUnknown::getIntegerSCEV(int Val, const Type *Ty) {
462 C = Constant::getNullValue(Ty);
463 else if (Ty->isFloatingPoint())
464 C = ConstantFP::get(Ty, Val);
465 else if (Ty->isSigned())
466 C = ConstantInt::get(Ty, Val);
468 C = ConstantInt::get(Ty->getSignedVersion(), Val);
469 C = ConstantExpr::getCast(C, Ty);
471 return SCEVUnknown::get(C);
474 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
475 /// input value to the specified type. If the type must be extended, it is zero
477 static SCEVHandle getTruncateOrZeroExtend(const SCEVHandle &V, const Type *Ty) {
478 const Type *SrcTy = V->getType();
479 assert(SrcTy->isInteger() && Ty->isInteger() &&
480 "Cannot truncate or zero extend with non-integer arguments!");
481 if (SrcTy->getPrimitiveSize() == Ty->getPrimitiveSize())
482 return V; // No conversion
483 if (SrcTy->getPrimitiveSize() > Ty->getPrimitiveSize())
484 return SCEVTruncateExpr::get(V, Ty);
485 return SCEVZeroExtendExpr::get(V, Ty);
488 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
490 SCEVHandle SCEV::getNegativeSCEV(const SCEVHandle &V) {
491 if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
492 return SCEVUnknown::get(ConstantExpr::getNeg(VC->getValue()));
494 return SCEVMulExpr::get(V, SCEVUnknown::getIntegerSCEV(-1, V->getType()));
497 /// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
499 SCEVHandle SCEV::getMinusSCEV(const SCEVHandle &LHS, const SCEVHandle &RHS) {
501 return SCEVAddExpr::get(LHS, SCEV::getNegativeSCEV(RHS));
505 /// PartialFact - Compute V!/(V-NumSteps)!
506 static SCEVHandle PartialFact(SCEVHandle V, unsigned NumSteps) {
507 // Handle this case efficiently, it is common to have constant iteration
508 // counts while computing loop exit values.
509 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(V)) {
510 uint64_t Val = SC->getValue()->getZExtValue();
512 for (; NumSteps; --NumSteps)
513 Result *= Val-(NumSteps-1);
514 Constant *Res = ConstantInt::get(Type::ULongTy, Result);
515 return SCEVUnknown::get(ConstantExpr::getCast(Res, V->getType()));
518 const Type *Ty = V->getType();
520 return SCEVUnknown::getIntegerSCEV(1, Ty);
522 SCEVHandle Result = V;
523 for (unsigned i = 1; i != NumSteps; ++i)
524 Result = SCEVMulExpr::get(Result, SCEV::getMinusSCEV(V,
525 SCEVUnknown::getIntegerSCEV(i, Ty)));
530 /// evaluateAtIteration - Return the value of this chain of recurrences at
531 /// the specified iteration number. We can evaluate this recurrence by
532 /// multiplying each element in the chain by the binomial coefficient
533 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
535 /// A*choose(It, 0) + B*choose(It, 1) + C*choose(It, 2) + D*choose(It, 3)
537 /// FIXME/VERIFY: I don't trust that this is correct in the face of overflow.
538 /// Is the binomial equation safe using modular arithmetic??
540 SCEVHandle SCEVAddRecExpr::evaluateAtIteration(SCEVHandle It) const {
541 SCEVHandle Result = getStart();
543 const Type *Ty = It->getType();
544 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
545 SCEVHandle BC = PartialFact(It, i);
547 SCEVHandle Val = SCEVSDivExpr::get(SCEVMulExpr::get(BC, getOperand(i)),
548 SCEVUnknown::getIntegerSCEV(Divisor,Ty));
549 Result = SCEVAddExpr::get(Result, Val);
555 //===----------------------------------------------------------------------===//
556 // SCEV Expression folder implementations
557 //===----------------------------------------------------------------------===//
559 SCEVHandle SCEVTruncateExpr::get(const SCEVHandle &Op, const Type *Ty) {
560 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
561 return SCEVUnknown::get(ConstantExpr::getCast(SC->getValue(), Ty));
563 // If the input value is a chrec scev made out of constants, truncate
564 // all of the constants.
565 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
566 std::vector<SCEVHandle> Operands;
567 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
568 // FIXME: This should allow truncation of other expression types!
569 if (isa<SCEVConstant>(AddRec->getOperand(i)))
570 Operands.push_back(get(AddRec->getOperand(i), Ty));
573 if (Operands.size() == AddRec->getNumOperands())
574 return SCEVAddRecExpr::get(Operands, AddRec->getLoop());
577 SCEVTruncateExpr *&Result = (*SCEVTruncates)[std::make_pair(Op, Ty)];
578 if (Result == 0) Result = new SCEVTruncateExpr(Op, Ty);
582 SCEVHandle SCEVZeroExtendExpr::get(const SCEVHandle &Op, const Type *Ty) {
583 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
584 return SCEVUnknown::get(ConstantExpr::getCast(SC->getValue(), Ty));
586 // FIXME: If the input value is a chrec scev, and we can prove that the value
587 // did not overflow the old, smaller, value, we can zero extend all of the
588 // operands (often constants). This would allow analysis of something like
589 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
591 SCEVZeroExtendExpr *&Result = (*SCEVZeroExtends)[std::make_pair(Op, Ty)];
592 if (Result == 0) Result = new SCEVZeroExtendExpr(Op, Ty);
596 // get - Get a canonical add expression, or something simpler if possible.
597 SCEVHandle SCEVAddExpr::get(std::vector<SCEVHandle> &Ops) {
598 assert(!Ops.empty() && "Cannot get empty add!");
599 if (Ops.size() == 1) return Ops[0];
601 // Sort by complexity, this groups all similar expression types together.
602 GroupByComplexity(Ops);
604 // If there are any constants, fold them together.
606 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
608 assert(Idx < Ops.size());
609 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
610 // We found two constants, fold them together!
611 Constant *Fold = ConstantExpr::getAdd(LHSC->getValue(), RHSC->getValue());
612 if (ConstantInt *CI = dyn_cast<ConstantInt>(Fold)) {
613 Ops[0] = SCEVConstant::get(CI);
614 Ops.erase(Ops.begin()+1); // Erase the folded element
615 if (Ops.size() == 1) return Ops[0];
616 LHSC = cast<SCEVConstant>(Ops[0]);
618 // If we couldn't fold the expression, move to the next constant. Note
619 // that this is impossible to happen in practice because we always
620 // constant fold constant ints to constant ints.
625 // If we are left with a constant zero being added, strip it off.
626 if (cast<SCEVConstant>(Ops[0])->getValue()->isNullValue()) {
627 Ops.erase(Ops.begin());
632 if (Ops.size() == 1) return Ops[0];
634 // Okay, check to see if the same value occurs in the operand list twice. If
635 // so, merge them together into an multiply expression. Since we sorted the
636 // list, these values are required to be adjacent.
637 const Type *Ty = Ops[0]->getType();
638 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
639 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
640 // Found a match, merge the two values into a multiply, and add any
641 // remaining values to the result.
642 SCEVHandle Two = SCEVUnknown::getIntegerSCEV(2, Ty);
643 SCEVHandle Mul = SCEVMulExpr::get(Ops[i], Two);
646 Ops.erase(Ops.begin()+i, Ops.begin()+i+2);
648 return SCEVAddExpr::get(Ops);
651 // Okay, now we know the first non-constant operand. If there are add
652 // operands they would be next.
653 if (Idx < Ops.size()) {
654 bool DeletedAdd = false;
655 while (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
656 // If we have an add, expand the add operands onto the end of the operands
658 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end());
659 Ops.erase(Ops.begin()+Idx);
663 // If we deleted at least one add, we added operands to the end of the list,
664 // and they are not necessarily sorted. Recurse to resort and resimplify
665 // any operands we just aquired.
670 // Skip over the add expression until we get to a multiply.
671 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
674 // If we are adding something to a multiply expression, make sure the
675 // something is not already an operand of the multiply. If so, merge it into
677 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
678 SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
679 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
680 SCEV *MulOpSCEV = Mul->getOperand(MulOp);
681 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
682 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(MulOpSCEV)) {
683 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
684 SCEVHandle InnerMul = Mul->getOperand(MulOp == 0);
685 if (Mul->getNumOperands() != 2) {
686 // If the multiply has more than two operands, we must get the
688 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end());
689 MulOps.erase(MulOps.begin()+MulOp);
690 InnerMul = SCEVMulExpr::get(MulOps);
692 SCEVHandle One = SCEVUnknown::getIntegerSCEV(1, Ty);
693 SCEVHandle AddOne = SCEVAddExpr::get(InnerMul, One);
694 SCEVHandle OuterMul = SCEVMulExpr::get(AddOne, Ops[AddOp]);
695 if (Ops.size() == 2) return OuterMul;
697 Ops.erase(Ops.begin()+AddOp);
698 Ops.erase(Ops.begin()+Idx-1);
700 Ops.erase(Ops.begin()+Idx);
701 Ops.erase(Ops.begin()+AddOp-1);
703 Ops.push_back(OuterMul);
704 return SCEVAddExpr::get(Ops);
707 // Check this multiply against other multiplies being added together.
708 for (unsigned OtherMulIdx = Idx+1;
709 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
711 SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
712 // If MulOp occurs in OtherMul, we can fold the two multiplies
714 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
715 OMulOp != e; ++OMulOp)
716 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
717 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
718 SCEVHandle InnerMul1 = Mul->getOperand(MulOp == 0);
719 if (Mul->getNumOperands() != 2) {
720 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end());
721 MulOps.erase(MulOps.begin()+MulOp);
722 InnerMul1 = SCEVMulExpr::get(MulOps);
724 SCEVHandle InnerMul2 = OtherMul->getOperand(OMulOp == 0);
725 if (OtherMul->getNumOperands() != 2) {
726 std::vector<SCEVHandle> MulOps(OtherMul->op_begin(),
728 MulOps.erase(MulOps.begin()+OMulOp);
729 InnerMul2 = SCEVMulExpr::get(MulOps);
731 SCEVHandle InnerMulSum = SCEVAddExpr::get(InnerMul1,InnerMul2);
732 SCEVHandle OuterMul = SCEVMulExpr::get(MulOpSCEV, InnerMulSum);
733 if (Ops.size() == 2) return OuterMul;
734 Ops.erase(Ops.begin()+Idx);
735 Ops.erase(Ops.begin()+OtherMulIdx-1);
736 Ops.push_back(OuterMul);
737 return SCEVAddExpr::get(Ops);
743 // If there are any add recurrences in the operands list, see if any other
744 // added values are loop invariant. If so, we can fold them into the
746 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
749 // Scan over all recurrences, trying to fold loop invariants into them.
750 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
751 // Scan all of the other operands to this add and add them to the vector if
752 // they are loop invariant w.r.t. the recurrence.
753 std::vector<SCEVHandle> LIOps;
754 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
755 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
756 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
757 LIOps.push_back(Ops[i]);
758 Ops.erase(Ops.begin()+i);
762 // If we found some loop invariants, fold them into the recurrence.
763 if (!LIOps.empty()) {
764 // NLI + LI + { Start,+,Step} --> NLI + { LI+Start,+,Step }
765 LIOps.push_back(AddRec->getStart());
767 std::vector<SCEVHandle> AddRecOps(AddRec->op_begin(), AddRec->op_end());
768 AddRecOps[0] = SCEVAddExpr::get(LIOps);
770 SCEVHandle NewRec = SCEVAddRecExpr::get(AddRecOps, AddRec->getLoop());
771 // If all of the other operands were loop invariant, we are done.
772 if (Ops.size() == 1) return NewRec;
774 // Otherwise, add the folded AddRec by the non-liv parts.
775 for (unsigned i = 0;; ++i)
776 if (Ops[i] == AddRec) {
780 return SCEVAddExpr::get(Ops);
783 // Okay, if there weren't any loop invariants to be folded, check to see if
784 // there are multiple AddRec's with the same loop induction variable being
785 // added together. If so, we can fold them.
786 for (unsigned OtherIdx = Idx+1;
787 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
788 if (OtherIdx != Idx) {
789 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
790 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
791 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D}
792 std::vector<SCEVHandle> NewOps(AddRec->op_begin(), AddRec->op_end());
793 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) {
794 if (i >= NewOps.size()) {
795 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i,
796 OtherAddRec->op_end());
799 NewOps[i] = SCEVAddExpr::get(NewOps[i], OtherAddRec->getOperand(i));
801 SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewOps, AddRec->getLoop());
803 if (Ops.size() == 2) return NewAddRec;
805 Ops.erase(Ops.begin()+Idx);
806 Ops.erase(Ops.begin()+OtherIdx-1);
807 Ops.push_back(NewAddRec);
808 return SCEVAddExpr::get(Ops);
812 // Otherwise couldn't fold anything into this recurrence. Move onto the
816 // Okay, it looks like we really DO need an add expr. Check to see if we
817 // already have one, otherwise create a new one.
818 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end());
819 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scAddExpr,
821 if (Result == 0) Result = new SCEVAddExpr(Ops);
826 SCEVHandle SCEVMulExpr::get(std::vector<SCEVHandle> &Ops) {
827 assert(!Ops.empty() && "Cannot get empty mul!");
829 // Sort by complexity, this groups all similar expression types together.
830 GroupByComplexity(Ops);
832 // If there are any constants, fold them together.
834 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
836 // C1*(C2+V) -> C1*C2 + C1*V
838 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
839 if (Add->getNumOperands() == 2 &&
840 isa<SCEVConstant>(Add->getOperand(0)))
841 return SCEVAddExpr::get(SCEVMulExpr::get(LHSC, Add->getOperand(0)),
842 SCEVMulExpr::get(LHSC, Add->getOperand(1)));
846 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
847 // We found two constants, fold them together!
848 Constant *Fold = ConstantExpr::getMul(LHSC->getValue(), RHSC->getValue());
849 if (ConstantInt *CI = dyn_cast<ConstantInt>(Fold)) {
850 Ops[0] = SCEVConstant::get(CI);
851 Ops.erase(Ops.begin()+1); // Erase the folded element
852 if (Ops.size() == 1) return Ops[0];
853 LHSC = cast<SCEVConstant>(Ops[0]);
855 // If we couldn't fold the expression, move to the next constant. Note
856 // that this is impossible to happen in practice because we always
857 // constant fold constant ints to constant ints.
862 // If we are left with a constant one being multiplied, strip it off.
863 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
864 Ops.erase(Ops.begin());
866 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isNullValue()) {
867 // If we have a multiply of zero, it will always be zero.
872 // Skip over the add expression until we get to a multiply.
873 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
879 // If there are mul operands inline them all into this expression.
880 if (Idx < Ops.size()) {
881 bool DeletedMul = false;
882 while (SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
883 // If we have an mul, expand the mul operands onto the end of the operands
885 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end());
886 Ops.erase(Ops.begin()+Idx);
890 // If we deleted at least one mul, we added operands to the end of the list,
891 // and they are not necessarily sorted. Recurse to resort and resimplify
892 // any operands we just aquired.
897 // If there are any add recurrences in the operands list, see if any other
898 // added values are loop invariant. If so, we can fold them into the
900 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
903 // Scan over all recurrences, trying to fold loop invariants into them.
904 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
905 // Scan all of the other operands to this mul and add them to the vector if
906 // they are loop invariant w.r.t. the recurrence.
907 std::vector<SCEVHandle> LIOps;
908 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
909 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
910 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
911 LIOps.push_back(Ops[i]);
912 Ops.erase(Ops.begin()+i);
916 // If we found some loop invariants, fold them into the recurrence.
917 if (!LIOps.empty()) {
918 // NLI * LI * { Start,+,Step} --> NLI * { LI*Start,+,LI*Step }
919 std::vector<SCEVHandle> NewOps;
920 NewOps.reserve(AddRec->getNumOperands());
921 if (LIOps.size() == 1) {
922 SCEV *Scale = LIOps[0];
923 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
924 NewOps.push_back(SCEVMulExpr::get(Scale, AddRec->getOperand(i)));
926 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
927 std::vector<SCEVHandle> MulOps(LIOps);
928 MulOps.push_back(AddRec->getOperand(i));
929 NewOps.push_back(SCEVMulExpr::get(MulOps));
933 SCEVHandle NewRec = SCEVAddRecExpr::get(NewOps, AddRec->getLoop());
935 // If all of the other operands were loop invariant, we are done.
936 if (Ops.size() == 1) return NewRec;
938 // Otherwise, multiply the folded AddRec by the non-liv parts.
939 for (unsigned i = 0;; ++i)
940 if (Ops[i] == AddRec) {
944 return SCEVMulExpr::get(Ops);
947 // Okay, if there weren't any loop invariants to be folded, check to see if
948 // there are multiple AddRec's with the same loop induction variable being
949 // multiplied together. If so, we can fold them.
950 for (unsigned OtherIdx = Idx+1;
951 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
952 if (OtherIdx != Idx) {
953 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
954 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
955 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D}
956 SCEVAddRecExpr *F = AddRec, *G = OtherAddRec;
957 SCEVHandle NewStart = SCEVMulExpr::get(F->getStart(),
959 SCEVHandle B = F->getStepRecurrence();
960 SCEVHandle D = G->getStepRecurrence();
961 SCEVHandle NewStep = SCEVAddExpr::get(SCEVMulExpr::get(F, D),
962 SCEVMulExpr::get(G, B),
963 SCEVMulExpr::get(B, D));
964 SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewStart, NewStep,
966 if (Ops.size() == 2) return NewAddRec;
968 Ops.erase(Ops.begin()+Idx);
969 Ops.erase(Ops.begin()+OtherIdx-1);
970 Ops.push_back(NewAddRec);
971 return SCEVMulExpr::get(Ops);
975 // Otherwise couldn't fold anything into this recurrence. Move onto the
979 // Okay, it looks like we really DO need an mul expr. Check to see if we
980 // already have one, otherwise create a new one.
981 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end());
982 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scMulExpr,
985 Result = new SCEVMulExpr(Ops);
989 SCEVHandle SCEVSDivExpr::get(const SCEVHandle &LHS, const SCEVHandle &RHS) {
990 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
991 if (RHSC->getValue()->equalsInt(1))
992 return LHS; // X /s 1 --> x
993 if (RHSC->getValue()->isAllOnesValue())
994 return SCEV::getNegativeSCEV(LHS); // X /s -1 --> -x
996 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
997 Constant *LHSCV = LHSC->getValue();
998 Constant *RHSCV = RHSC->getValue();
999 if (LHSCV->getType()->isUnsigned())
1000 LHSCV = ConstantExpr::getCast(LHSCV,
1001 LHSCV->getType()->getSignedVersion());
1002 if (RHSCV->getType()->isUnsigned())
1003 RHSCV = ConstantExpr::getCast(RHSCV, LHSCV->getType());
1004 return SCEVUnknown::get(ConstantExpr::getDiv(LHSCV, RHSCV));
1008 // FIXME: implement folding of (X*4)/4 when we know X*4 doesn't overflow.
1010 SCEVSDivExpr *&Result = (*SCEVSDivs)[std::make_pair(LHS, RHS)];
1011 if (Result == 0) Result = new SCEVSDivExpr(LHS, RHS);
1016 /// SCEVAddRecExpr::get - Get a add recurrence expression for the
1017 /// specified loop. Simplify the expression as much as possible.
1018 SCEVHandle SCEVAddRecExpr::get(const SCEVHandle &Start,
1019 const SCEVHandle &Step, const Loop *L) {
1020 std::vector<SCEVHandle> Operands;
1021 Operands.push_back(Start);
1022 if (SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
1023 if (StepChrec->getLoop() == L) {
1024 Operands.insert(Operands.end(), StepChrec->op_begin(),
1025 StepChrec->op_end());
1026 return get(Operands, L);
1029 Operands.push_back(Step);
1030 return get(Operands, L);
1033 /// SCEVAddRecExpr::get - Get a add recurrence expression for the
1034 /// specified loop. Simplify the expression as much as possible.
1035 SCEVHandle SCEVAddRecExpr::get(std::vector<SCEVHandle> &Operands,
1037 if (Operands.size() == 1) return Operands[0];
1039 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Operands.back()))
1040 if (StepC->getValue()->isNullValue()) {
1041 Operands.pop_back();
1042 return get(Operands, L); // { X,+,0 } --> X
1045 SCEVAddRecExpr *&Result =
1046 (*SCEVAddRecExprs)[std::make_pair(L, std::vector<SCEV*>(Operands.begin(),
1048 if (Result == 0) Result = new SCEVAddRecExpr(Operands, L);
1052 SCEVHandle SCEVUnknown::get(Value *V) {
1053 if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
1054 return SCEVConstant::get(CI);
1055 SCEVUnknown *&Result = (*SCEVUnknowns)[V];
1056 if (Result == 0) Result = new SCEVUnknown(V);
1061 //===----------------------------------------------------------------------===//
1062 // ScalarEvolutionsImpl Definition and Implementation
1063 //===----------------------------------------------------------------------===//
1065 /// ScalarEvolutionsImpl - This class implements the main driver for the scalar
1069 struct VISIBILITY_HIDDEN ScalarEvolutionsImpl {
1070 /// F - The function we are analyzing.
1074 /// LI - The loop information for the function we are currently analyzing.
1078 /// UnknownValue - This SCEV is used to represent unknown trip counts and
1080 SCEVHandle UnknownValue;
1082 /// Scalars - This is a cache of the scalars we have analyzed so far.
1084 std::map<Value*, SCEVHandle> Scalars;
1086 /// IterationCounts - Cache the iteration count of the loops for this
1087 /// function as they are computed.
1088 std::map<const Loop*, SCEVHandle> IterationCounts;
1090 /// ConstantEvolutionLoopExitValue - This map contains entries for all of
1091 /// the PHI instructions that we attempt to compute constant evolutions for.
1092 /// This allows us to avoid potentially expensive recomputation of these
1093 /// properties. An instruction maps to null if we are unable to compute its
1095 std::map<PHINode*, Constant*> ConstantEvolutionLoopExitValue;
1098 ScalarEvolutionsImpl(Function &f, LoopInfo &li)
1099 : F(f), LI(li), UnknownValue(new SCEVCouldNotCompute()) {}
1101 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
1102 /// expression and create a new one.
1103 SCEVHandle getSCEV(Value *V);
1105 /// hasSCEV - Return true if the SCEV for this value has already been
1107 bool hasSCEV(Value *V) const {
1108 return Scalars.count(V);
1111 /// setSCEV - Insert the specified SCEV into the map of current SCEVs for
1112 /// the specified value.
1113 void setSCEV(Value *V, const SCEVHandle &H) {
1114 bool isNew = Scalars.insert(std::make_pair(V, H)).second;
1115 assert(isNew && "This entry already existed!");
1119 /// getSCEVAtScope - Compute the value of the specified expression within
1120 /// the indicated loop (which may be null to indicate in no loop). If the
1121 /// expression cannot be evaluated, return UnknownValue itself.
1122 SCEVHandle getSCEVAtScope(SCEV *V, const Loop *L);
1125 /// hasLoopInvariantIterationCount - Return true if the specified loop has
1126 /// an analyzable loop-invariant iteration count.
1127 bool hasLoopInvariantIterationCount(const Loop *L);
1129 /// getIterationCount - If the specified loop has a predictable iteration
1130 /// count, return it. Note that it is not valid to call this method on a
1131 /// loop without a loop-invariant iteration count.
1132 SCEVHandle getIterationCount(const Loop *L);
1134 /// deleteInstructionFromRecords - This method should be called by the
1135 /// client before it removes an instruction from the program, to make sure
1136 /// that no dangling references are left around.
1137 void deleteInstructionFromRecords(Instruction *I);
1140 /// createSCEV - We know that there is no SCEV for the specified value.
1141 /// Analyze the expression.
1142 SCEVHandle createSCEV(Value *V);
1143 SCEVHandle createNodeForCast(CastInst *CI);
1145 /// createNodeForPHI - Provide the special handling we need to analyze PHI
1147 SCEVHandle createNodeForPHI(PHINode *PN);
1149 /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value
1150 /// for the specified instruction and replaces any references to the
1151 /// symbolic value SymName with the specified value. This is used during
1153 void ReplaceSymbolicValueWithConcrete(Instruction *I,
1154 const SCEVHandle &SymName,
1155 const SCEVHandle &NewVal);
1157 /// ComputeIterationCount - Compute the number of times the specified loop
1159 SCEVHandle ComputeIterationCount(const Loop *L);
1161 /// ComputeLoadConstantCompareIterationCount - Given an exit condition of
1162 /// 'setcc load X, cst', try to se if we can compute the trip count.
1163 SCEVHandle ComputeLoadConstantCompareIterationCount(LoadInst *LI,
1166 unsigned SetCCOpcode);
1168 /// ComputeIterationCountExhaustively - If the trip is known to execute a
1169 /// constant number of times (the condition evolves only from constants),
1170 /// try to evaluate a few iterations of the loop until we get the exit
1171 /// condition gets a value of ExitWhen (true or false). If we cannot
1172 /// evaluate the trip count of the loop, return UnknownValue.
1173 SCEVHandle ComputeIterationCountExhaustively(const Loop *L, Value *Cond,
1176 /// HowFarToZero - Return the number of times a backedge comparing the
1177 /// specified value to zero will execute. If not computable, return
1179 SCEVHandle HowFarToZero(SCEV *V, const Loop *L);
1181 /// HowFarToNonZero - Return the number of times a backedge checking the
1182 /// specified value for nonzero will execute. If not computable, return
1184 SCEVHandle HowFarToNonZero(SCEV *V, const Loop *L);
1186 /// HowManyLessThans - Return the number of times a backedge containing the
1187 /// specified less-than comparison will execute. If not computable, return
1189 SCEVHandle HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L);
1191 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
1192 /// in the header of its containing loop, we know the loop executes a
1193 /// constant number of times, and the PHI node is just a recurrence
1194 /// involving constants, fold it.
1195 Constant *getConstantEvolutionLoopExitValue(PHINode *PN, uint64_t Its,
1200 //===----------------------------------------------------------------------===//
1201 // Basic SCEV Analysis and PHI Idiom Recognition Code
1204 /// deleteInstructionFromRecords - This method should be called by the
1205 /// client before it removes an instruction from the program, to make sure
1206 /// that no dangling references are left around.
1207 void ScalarEvolutionsImpl::deleteInstructionFromRecords(Instruction *I) {
1209 if (PHINode *PN = dyn_cast<PHINode>(I))
1210 ConstantEvolutionLoopExitValue.erase(PN);
1214 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
1215 /// expression and create a new one.
1216 SCEVHandle ScalarEvolutionsImpl::getSCEV(Value *V) {
1217 assert(V->getType() != Type::VoidTy && "Can't analyze void expressions!");
1219 std::map<Value*, SCEVHandle>::iterator I = Scalars.find(V);
1220 if (I != Scalars.end()) return I->second;
1221 SCEVHandle S = createSCEV(V);
1222 Scalars.insert(std::make_pair(V, S));
1226 /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for
1227 /// the specified instruction and replaces any references to the symbolic value
1228 /// SymName with the specified value. This is used during PHI resolution.
1229 void ScalarEvolutionsImpl::
1230 ReplaceSymbolicValueWithConcrete(Instruction *I, const SCEVHandle &SymName,
1231 const SCEVHandle &NewVal) {
1232 std::map<Value*, SCEVHandle>::iterator SI = Scalars.find(I);
1233 if (SI == Scalars.end()) return;
1236 SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal);
1237 if (NV == SI->second) return; // No change.
1239 SI->second = NV; // Update the scalars map!
1241 // Any instruction values that use this instruction might also need to be
1243 for (Value::use_iterator UI = I->use_begin(), E = I->use_end();
1245 ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal);
1248 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
1249 /// a loop header, making it a potential recurrence, or it doesn't.
1251 SCEVHandle ScalarEvolutionsImpl::createNodeForPHI(PHINode *PN) {
1252 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized.
1253 if (const Loop *L = LI.getLoopFor(PN->getParent()))
1254 if (L->getHeader() == PN->getParent()) {
1255 // If it lives in the loop header, it has two incoming values, one
1256 // from outside the loop, and one from inside.
1257 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0));
1258 unsigned BackEdge = IncomingEdge^1;
1260 // While we are analyzing this PHI node, handle its value symbolically.
1261 SCEVHandle SymbolicName = SCEVUnknown::get(PN);
1262 assert(Scalars.find(PN) == Scalars.end() &&
1263 "PHI node already processed?");
1264 Scalars.insert(std::make_pair(PN, SymbolicName));
1266 // Using this symbolic name for the PHI, analyze the value coming around
1268 SCEVHandle BEValue = getSCEV(PN->getIncomingValue(BackEdge));
1270 // NOTE: If BEValue is loop invariant, we know that the PHI node just
1271 // has a special value for the first iteration of the loop.
1273 // If the value coming around the backedge is an add with the symbolic
1274 // value we just inserted, then we found a simple induction variable!
1275 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
1276 // If there is a single occurrence of the symbolic value, replace it
1277 // with a recurrence.
1278 unsigned FoundIndex = Add->getNumOperands();
1279 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
1280 if (Add->getOperand(i) == SymbolicName)
1281 if (FoundIndex == e) {
1286 if (FoundIndex != Add->getNumOperands()) {
1287 // Create an add with everything but the specified operand.
1288 std::vector<SCEVHandle> Ops;
1289 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
1290 if (i != FoundIndex)
1291 Ops.push_back(Add->getOperand(i));
1292 SCEVHandle Accum = SCEVAddExpr::get(Ops);
1294 // This is not a valid addrec if the step amount is varying each
1295 // loop iteration, but is not itself an addrec in this loop.
1296 if (Accum->isLoopInvariant(L) ||
1297 (isa<SCEVAddRecExpr>(Accum) &&
1298 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
1299 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
1300 SCEVHandle PHISCEV = SCEVAddRecExpr::get(StartVal, Accum, L);
1302 // Okay, for the entire analysis of this edge we assumed the PHI
1303 // to be symbolic. We now need to go back and update all of the
1304 // entries for the scalars that use the PHI (except for the PHI
1305 // itself) to use the new analyzed value instead of the "symbolic"
1307 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
1311 } else if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(BEValue)) {
1312 // Otherwise, this could be a loop like this:
1313 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
1314 // In this case, j = {1,+,1} and BEValue is j.
1315 // Because the other in-value of i (0) fits the evolution of BEValue
1316 // i really is an addrec evolution.
1317 if (AddRec->getLoop() == L && AddRec->isAffine()) {
1318 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
1320 // If StartVal = j.start - j.stride, we can use StartVal as the
1321 // initial step of the addrec evolution.
1322 if (StartVal == SCEV::getMinusSCEV(AddRec->getOperand(0),
1323 AddRec->getOperand(1))) {
1324 SCEVHandle PHISCEV =
1325 SCEVAddRecExpr::get(StartVal, AddRec->getOperand(1), L);
1327 // Okay, for the entire analysis of this edge we assumed the PHI
1328 // to be symbolic. We now need to go back and update all of the
1329 // entries for the scalars that use the PHI (except for the PHI
1330 // itself) to use the new analyzed value instead of the "symbolic"
1332 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
1338 return SymbolicName;
1341 // If it's not a loop phi, we can't handle it yet.
1342 return SCEVUnknown::get(PN);
1345 /// createNodeForCast - Handle the various forms of casts that we support.
1347 SCEVHandle ScalarEvolutionsImpl::createNodeForCast(CastInst *CI) {
1348 const Type *SrcTy = CI->getOperand(0)->getType();
1349 const Type *DestTy = CI->getType();
1351 // If this is a noop cast (ie, conversion from int to uint), ignore it.
1352 if (SrcTy->isLosslesslyConvertibleTo(DestTy))
1353 return getSCEV(CI->getOperand(0));
1355 if (SrcTy->isInteger() && DestTy->isInteger()) {
1356 // Otherwise, if this is a truncating integer cast, we can represent this
1358 if (SrcTy->getPrimitiveSize() > DestTy->getPrimitiveSize())
1359 return SCEVTruncateExpr::get(getSCEV(CI->getOperand(0)),
1360 CI->getType()->getUnsignedVersion());
1361 if (SrcTy->isUnsigned() &&
1362 SrcTy->getPrimitiveSize() > DestTy->getPrimitiveSize())
1363 return SCEVZeroExtendExpr::get(getSCEV(CI->getOperand(0)),
1364 CI->getType()->getUnsignedVersion());
1367 // If this is an sign or zero extending cast and we can prove that the value
1368 // will never overflow, we could do similar transformations.
1370 // Otherwise, we can't handle this cast!
1371 return SCEVUnknown::get(CI);
1375 /// createSCEV - We know that there is no SCEV for the specified value.
1376 /// Analyze the expression.
1378 SCEVHandle ScalarEvolutionsImpl::createSCEV(Value *V) {
1379 if (Instruction *I = dyn_cast<Instruction>(V)) {
1380 switch (I->getOpcode()) {
1381 case Instruction::Add:
1382 return SCEVAddExpr::get(getSCEV(I->getOperand(0)),
1383 getSCEV(I->getOperand(1)));
1384 case Instruction::Mul:
1385 return SCEVMulExpr::get(getSCEV(I->getOperand(0)),
1386 getSCEV(I->getOperand(1)));
1387 case Instruction::Div:
1388 if (V->getType()->isInteger() && V->getType()->isSigned())
1389 return SCEVSDivExpr::get(getSCEV(I->getOperand(0)),
1390 getSCEV(I->getOperand(1)));
1393 case Instruction::Sub:
1394 return SCEV::getMinusSCEV(getSCEV(I->getOperand(0)),
1395 getSCEV(I->getOperand(1)));
1397 case Instruction::Shl:
1398 // Turn shift left of a constant amount into a multiply.
1399 if (ConstantInt *SA = dyn_cast<ConstantInt>(I->getOperand(1))) {
1400 Constant *X = ConstantInt::get(V->getType(), 1);
1401 X = ConstantExpr::getShl(X, SA);
1402 return SCEVMulExpr::get(getSCEV(I->getOperand(0)), getSCEV(X));
1406 case Instruction::Cast:
1407 return createNodeForCast(cast<CastInst>(I));
1409 case Instruction::PHI:
1410 return createNodeForPHI(cast<PHINode>(I));
1412 default: // We cannot analyze this expression.
1417 return SCEVUnknown::get(V);
1422 //===----------------------------------------------------------------------===//
1423 // Iteration Count Computation Code
1426 /// getIterationCount - If the specified loop has a predictable iteration
1427 /// count, return it. Note that it is not valid to call this method on a
1428 /// loop without a loop-invariant iteration count.
1429 SCEVHandle ScalarEvolutionsImpl::getIterationCount(const Loop *L) {
1430 std::map<const Loop*, SCEVHandle>::iterator I = IterationCounts.find(L);
1431 if (I == IterationCounts.end()) {
1432 SCEVHandle ItCount = ComputeIterationCount(L);
1433 I = IterationCounts.insert(std::make_pair(L, ItCount)).first;
1434 if (ItCount != UnknownValue) {
1435 assert(ItCount->isLoopInvariant(L) &&
1436 "Computed trip count isn't loop invariant for loop!");
1437 ++NumTripCountsComputed;
1438 } else if (isa<PHINode>(L->getHeader()->begin())) {
1439 // Only count loops that have phi nodes as not being computable.
1440 ++NumTripCountsNotComputed;
1446 /// ComputeIterationCount - Compute the number of times the specified loop
1448 SCEVHandle ScalarEvolutionsImpl::ComputeIterationCount(const Loop *L) {
1449 // If the loop has a non-one exit block count, we can't analyze it.
1450 std::vector<BasicBlock*> ExitBlocks;
1451 L->getExitBlocks(ExitBlocks);
1452 if (ExitBlocks.size() != 1) return UnknownValue;
1454 // Okay, there is one exit block. Try to find the condition that causes the
1455 // loop to be exited.
1456 BasicBlock *ExitBlock = ExitBlocks[0];
1458 BasicBlock *ExitingBlock = 0;
1459 for (pred_iterator PI = pred_begin(ExitBlock), E = pred_end(ExitBlock);
1461 if (L->contains(*PI)) {
1462 if (ExitingBlock == 0)
1465 return UnknownValue; // More than one block exiting!
1467 assert(ExitingBlock && "No exits from loop, something is broken!");
1469 // Okay, we've computed the exiting block. See what condition causes us to
1472 // FIXME: we should be able to handle switch instructions (with a single exit)
1473 // FIXME: We should handle cast of int to bool as well
1474 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
1475 if (ExitBr == 0) return UnknownValue;
1476 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
1477 SetCondInst *ExitCond = dyn_cast<SetCondInst>(ExitBr->getCondition());
1478 if (ExitCond == 0) // Not a setcc
1479 return ComputeIterationCountExhaustively(L, ExitBr->getCondition(),
1480 ExitBr->getSuccessor(0) == ExitBlock);
1482 // If the condition was exit on true, convert the condition to exit on false.
1483 Instruction::BinaryOps Cond;
1484 if (ExitBr->getSuccessor(1) == ExitBlock)
1485 Cond = ExitCond->getOpcode();
1487 Cond = ExitCond->getInverseCondition();
1489 // Handle common loops like: for (X = "string"; *X; ++X)
1490 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
1491 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
1493 ComputeLoadConstantCompareIterationCount(LI, RHS, L, Cond);
1494 if (!isa<SCEVCouldNotCompute>(ItCnt)) return ItCnt;
1497 SCEVHandle LHS = getSCEV(ExitCond->getOperand(0));
1498 SCEVHandle RHS = getSCEV(ExitCond->getOperand(1));
1500 // Try to evaluate any dependencies out of the loop.
1501 SCEVHandle Tmp = getSCEVAtScope(LHS, L);
1502 if (!isa<SCEVCouldNotCompute>(Tmp)) LHS = Tmp;
1503 Tmp = getSCEVAtScope(RHS, L);
1504 if (!isa<SCEVCouldNotCompute>(Tmp)) RHS = Tmp;
1506 // At this point, we would like to compute how many iterations of the loop the
1507 // predicate will return true for these inputs.
1508 if (isa<SCEVConstant>(LHS) && !isa<SCEVConstant>(RHS)) {
1509 // If there is a constant, force it into the RHS.
1510 std::swap(LHS, RHS);
1511 Cond = SetCondInst::getSwappedCondition(Cond);
1514 // FIXME: think about handling pointer comparisons! i.e.:
1515 // while (P != P+100) ++P;
1517 // If we have a comparison of a chrec against a constant, try to use value
1518 // ranges to answer this query.
1519 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
1520 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
1521 if (AddRec->getLoop() == L) {
1522 // Form the comparison range using the constant of the correct type so
1523 // that the ConstantRange class knows to do a signed or unsigned
1525 ConstantInt *CompVal = RHSC->getValue();
1526 const Type *RealTy = ExitCond->getOperand(0)->getType();
1527 CompVal = dyn_cast<ConstantInt>(ConstantExpr::getCast(CompVal, RealTy));
1529 // Form the constant range.
1530 ConstantRange CompRange(Cond, CompVal);
1532 // Now that we have it, if it's signed, convert it to an unsigned
1534 if (CompRange.getLower()->getType()->isSigned()) {
1535 const Type *NewTy = RHSC->getValue()->getType();
1536 Constant *NewL = ConstantExpr::getCast(CompRange.getLower(), NewTy);
1537 Constant *NewU = ConstantExpr::getCast(CompRange.getUpper(), NewTy);
1538 CompRange = ConstantRange(NewL, NewU);
1541 SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange);
1542 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
1547 case Instruction::SetNE: // while (X != Y)
1548 // Convert to: while (X-Y != 0)
1549 if (LHS->getType()->isInteger()) {
1550 SCEVHandle TC = HowFarToZero(SCEV::getMinusSCEV(LHS, RHS), L);
1551 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
1554 case Instruction::SetEQ:
1555 // Convert to: while (X-Y == 0) // while (X == Y)
1556 if (LHS->getType()->isInteger()) {
1557 SCEVHandle TC = HowFarToNonZero(SCEV::getMinusSCEV(LHS, RHS), L);
1558 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
1561 case Instruction::SetLT:
1562 if (LHS->getType()->isInteger() &&
1563 ExitCond->getOperand(0)->getType()->isSigned()) {
1564 SCEVHandle TC = HowManyLessThans(LHS, RHS, L);
1565 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
1568 case Instruction::SetGT:
1569 if (LHS->getType()->isInteger() &&
1570 ExitCond->getOperand(0)->getType()->isSigned()) {
1571 SCEVHandle TC = HowManyLessThans(RHS, LHS, L);
1572 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
1577 std::cerr << "ComputeIterationCount ";
1578 if (ExitCond->getOperand(0)->getType()->isUnsigned())
1579 std::cerr << "[unsigned] ";
1580 std::cerr << *LHS << " "
1581 << Instruction::getOpcodeName(Cond) << " " << *RHS << "\n";
1586 return ComputeIterationCountExhaustively(L, ExitCond,
1587 ExitBr->getSuccessor(0) == ExitBlock);
1590 static ConstantInt *
1591 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, Constant *C) {
1592 SCEVHandle InVal = SCEVConstant::get(cast<ConstantInt>(C));
1593 SCEVHandle Val = AddRec->evaluateAtIteration(InVal);
1594 assert(isa<SCEVConstant>(Val) &&
1595 "Evaluation of SCEV at constant didn't fold correctly?");
1596 return cast<SCEVConstant>(Val)->getValue();
1599 /// GetAddressedElementFromGlobal - Given a global variable with an initializer
1600 /// and a GEP expression (missing the pointer index) indexing into it, return
1601 /// the addressed element of the initializer or null if the index expression is
1604 GetAddressedElementFromGlobal(GlobalVariable *GV,
1605 const std::vector<ConstantInt*> &Indices) {
1606 Constant *Init = GV->getInitializer();
1607 for (unsigned i = 0, e = Indices.size(); i != e; ++i) {
1608 uint64_t Idx = Indices[i]->getZExtValue();
1609 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) {
1610 assert(Idx < CS->getNumOperands() && "Bad struct index!");
1611 Init = cast<Constant>(CS->getOperand(Idx));
1612 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) {
1613 if (Idx >= CA->getNumOperands()) return 0; // Bogus program
1614 Init = cast<Constant>(CA->getOperand(Idx));
1615 } else if (isa<ConstantAggregateZero>(Init)) {
1616 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) {
1617 assert(Idx < STy->getNumElements() && "Bad struct index!");
1618 Init = Constant::getNullValue(STy->getElementType(Idx));
1619 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) {
1620 if (Idx >= ATy->getNumElements()) return 0; // Bogus program
1621 Init = Constant::getNullValue(ATy->getElementType());
1623 assert(0 && "Unknown constant aggregate type!");
1627 return 0; // Unknown initializer type
1633 /// ComputeLoadConstantCompareIterationCount - Given an exit condition of
1634 /// 'setcc load X, cst', try to se if we can compute the trip count.
1635 SCEVHandle ScalarEvolutionsImpl::
1636 ComputeLoadConstantCompareIterationCount(LoadInst *LI, Constant *RHS,
1637 const Loop *L, unsigned SetCCOpcode) {
1638 if (LI->isVolatile()) return UnknownValue;
1640 // Check to see if the loaded pointer is a getelementptr of a global.
1641 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
1642 if (!GEP) return UnknownValue;
1644 // Make sure that it is really a constant global we are gepping, with an
1645 // initializer, and make sure the first IDX is really 0.
1646 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
1647 if (!GV || !GV->isConstant() || !GV->hasInitializer() ||
1648 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
1649 !cast<Constant>(GEP->getOperand(1))->isNullValue())
1650 return UnknownValue;
1652 // Okay, we allow one non-constant index into the GEP instruction.
1654 std::vector<ConstantInt*> Indexes;
1655 unsigned VarIdxNum = 0;
1656 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
1657 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
1658 Indexes.push_back(CI);
1659 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
1660 if (VarIdx) return UnknownValue; // Multiple non-constant idx's.
1661 VarIdx = GEP->getOperand(i);
1663 Indexes.push_back(0);
1666 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
1667 // Check to see if X is a loop variant variable value now.
1668 SCEVHandle Idx = getSCEV(VarIdx);
1669 SCEVHandle Tmp = getSCEVAtScope(Idx, L);
1670 if (!isa<SCEVCouldNotCompute>(Tmp)) Idx = Tmp;
1672 // We can only recognize very limited forms of loop index expressions, in
1673 // particular, only affine AddRec's like {C1,+,C2}.
1674 SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
1675 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) ||
1676 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
1677 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
1678 return UnknownValue;
1680 unsigned MaxSteps = MaxBruteForceIterations;
1681 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
1682 ConstantInt *ItCst =
1683 ConstantInt::get(IdxExpr->getType()->getUnsignedVersion(), IterationNum);
1684 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst);
1686 // Form the GEP offset.
1687 Indexes[VarIdxNum] = Val;
1689 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes);
1690 if (Result == 0) break; // Cannot compute!
1692 // Evaluate the condition for this iteration.
1693 Result = ConstantExpr::get(SetCCOpcode, Result, RHS);
1694 if (!isa<ConstantBool>(Result)) break; // Couldn't decide for sure
1695 if (cast<ConstantBool>(Result)->getValue() == false) {
1697 std::cerr << "\n***\n*** Computed loop count " << *ItCst
1698 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
1701 ++NumArrayLenItCounts;
1702 return SCEVConstant::get(ItCst); // Found terminating iteration!
1705 return UnknownValue;
1709 /// CanConstantFold - Return true if we can constant fold an instruction of the
1710 /// specified type, assuming that all operands were constants.
1711 static bool CanConstantFold(const Instruction *I) {
1712 if (isa<BinaryOperator>(I) || isa<ShiftInst>(I) ||
1713 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I))
1716 if (const CallInst *CI = dyn_cast<CallInst>(I))
1717 if (const Function *F = CI->getCalledFunction())
1718 return canConstantFoldCallTo((Function*)F); // FIXME: elim cast
1722 /// ConstantFold - Constant fold an instruction of the specified type with the
1723 /// specified constant operands. This function may modify the operands vector.
1724 static Constant *ConstantFold(const Instruction *I,
1725 std::vector<Constant*> &Operands) {
1726 if (isa<BinaryOperator>(I) || isa<ShiftInst>(I))
1727 return ConstantExpr::get(I->getOpcode(), Operands[0], Operands[1]);
1729 switch (I->getOpcode()) {
1730 case Instruction::Cast:
1731 return ConstantExpr::getCast(Operands[0], I->getType());
1732 case Instruction::Select:
1733 return ConstantExpr::getSelect(Operands[0], Operands[1], Operands[2]);
1734 case Instruction::Call:
1735 if (Function *GV = dyn_cast<Function>(Operands[0])) {
1736 Operands.erase(Operands.begin());
1737 return ConstantFoldCall(cast<Function>(GV), Operands);
1741 case Instruction::GetElementPtr:
1742 Constant *Base = Operands[0];
1743 Operands.erase(Operands.begin());
1744 return ConstantExpr::getGetElementPtr(Base, Operands);
1750 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
1751 /// in the loop that V is derived from. We allow arbitrary operations along the
1752 /// way, but the operands of an operation must either be constants or a value
1753 /// derived from a constant PHI. If this expression does not fit with these
1754 /// constraints, return null.
1755 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
1756 // If this is not an instruction, or if this is an instruction outside of the
1757 // loop, it can't be derived from a loop PHI.
1758 Instruction *I = dyn_cast<Instruction>(V);
1759 if (I == 0 || !L->contains(I->getParent())) return 0;
1761 if (PHINode *PN = dyn_cast<PHINode>(I))
1762 if (L->getHeader() == I->getParent())
1765 // We don't currently keep track of the control flow needed to evaluate
1766 // PHIs, so we cannot handle PHIs inside of loops.
1769 // If we won't be able to constant fold this expression even if the operands
1770 // are constants, return early.
1771 if (!CanConstantFold(I)) return 0;
1773 // Otherwise, we can evaluate this instruction if all of its operands are
1774 // constant or derived from a PHI node themselves.
1776 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op)
1777 if (!(isa<Constant>(I->getOperand(Op)) ||
1778 isa<GlobalValue>(I->getOperand(Op)))) {
1779 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L);
1780 if (P == 0) return 0; // Not evolving from PHI
1784 return 0; // Evolving from multiple different PHIs.
1787 // This is a expression evolving from a constant PHI!
1791 /// EvaluateExpression - Given an expression that passes the
1792 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
1793 /// in the loop has the value PHIVal. If we can't fold this expression for some
1794 /// reason, return null.
1795 static Constant *EvaluateExpression(Value *V, Constant *PHIVal) {
1796 if (isa<PHINode>(V)) return PHIVal;
1797 if (GlobalValue *GV = dyn_cast<GlobalValue>(V))
1799 if (Constant *C = dyn_cast<Constant>(V)) return C;
1800 Instruction *I = cast<Instruction>(V);
1802 std::vector<Constant*> Operands;
1803 Operands.resize(I->getNumOperands());
1805 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
1806 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal);
1807 if (Operands[i] == 0) return 0;
1810 return ConstantFold(I, Operands);
1813 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
1814 /// in the header of its containing loop, we know the loop executes a
1815 /// constant number of times, and the PHI node is just a recurrence
1816 /// involving constants, fold it.
1817 Constant *ScalarEvolutionsImpl::
1818 getConstantEvolutionLoopExitValue(PHINode *PN, uint64_t Its, const Loop *L) {
1819 std::map<PHINode*, Constant*>::iterator I =
1820 ConstantEvolutionLoopExitValue.find(PN);
1821 if (I != ConstantEvolutionLoopExitValue.end())
1824 if (Its > MaxBruteForceIterations)
1825 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
1827 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
1829 // Since the loop is canonicalized, the PHI node must have two entries. One
1830 // entry must be a constant (coming in from outside of the loop), and the
1831 // second must be derived from the same PHI.
1832 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
1833 Constant *StartCST =
1834 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
1836 return RetVal = 0; // Must be a constant.
1838 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
1839 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
1841 return RetVal = 0; // Not derived from same PHI.
1843 // Execute the loop symbolically to determine the exit value.
1844 unsigned IterationNum = 0;
1845 unsigned NumIterations = Its;
1846 if (NumIterations != Its)
1847 return RetVal = 0; // More than 2^32 iterations??
1849 for (Constant *PHIVal = StartCST; ; ++IterationNum) {
1850 if (IterationNum == NumIterations)
1851 return RetVal = PHIVal; // Got exit value!
1853 // Compute the value of the PHI node for the next iteration.
1854 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
1855 if (NextPHI == PHIVal)
1856 return RetVal = NextPHI; // Stopped evolving!
1858 return 0; // Couldn't evaluate!
1863 /// ComputeIterationCountExhaustively - If the trip is known to execute a
1864 /// constant number of times (the condition evolves only from constants),
1865 /// try to evaluate a few iterations of the loop until we get the exit
1866 /// condition gets a value of ExitWhen (true or false). If we cannot
1867 /// evaluate the trip count of the loop, return UnknownValue.
1868 SCEVHandle ScalarEvolutionsImpl::
1869 ComputeIterationCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) {
1870 PHINode *PN = getConstantEvolvingPHI(Cond, L);
1871 if (PN == 0) return UnknownValue;
1873 // Since the loop is canonicalized, the PHI node must have two entries. One
1874 // entry must be a constant (coming in from outside of the loop), and the
1875 // second must be derived from the same PHI.
1876 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
1877 Constant *StartCST =
1878 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
1879 if (StartCST == 0) return UnknownValue; // Must be a constant.
1881 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
1882 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
1883 if (PN2 != PN) return UnknownValue; // Not derived from same PHI.
1885 // Okay, we find a PHI node that defines the trip count of this loop. Execute
1886 // the loop symbolically to determine when the condition gets a value of
1888 unsigned IterationNum = 0;
1889 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
1890 for (Constant *PHIVal = StartCST;
1891 IterationNum != MaxIterations; ++IterationNum) {
1892 ConstantBool *CondVal =
1893 dyn_cast_or_null<ConstantBool>(EvaluateExpression(Cond, PHIVal));
1894 if (!CondVal) return UnknownValue; // Couldn't symbolically evaluate.
1896 if (CondVal->getValue() == ExitWhen) {
1897 ConstantEvolutionLoopExitValue[PN] = PHIVal;
1898 ++NumBruteForceTripCountsComputed;
1899 return SCEVConstant::get(ConstantInt::get(Type::UIntTy, IterationNum));
1902 // Compute the value of the PHI node for the next iteration.
1903 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
1904 if (NextPHI == 0 || NextPHI == PHIVal)
1905 return UnknownValue; // Couldn't evaluate or not making progress...
1909 // Too many iterations were needed to evaluate.
1910 return UnknownValue;
1913 /// getSCEVAtScope - Compute the value of the specified expression within the
1914 /// indicated loop (which may be null to indicate in no loop). If the
1915 /// expression cannot be evaluated, return UnknownValue.
1916 SCEVHandle ScalarEvolutionsImpl::getSCEVAtScope(SCEV *V, const Loop *L) {
1917 // FIXME: this should be turned into a virtual method on SCEV!
1919 if (isa<SCEVConstant>(V)) return V;
1921 // If this instruction is evolves from a constant-evolving PHI, compute the
1922 // exit value from the loop without using SCEVs.
1923 if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
1924 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
1925 const Loop *LI = this->LI[I->getParent()];
1926 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
1927 if (PHINode *PN = dyn_cast<PHINode>(I))
1928 if (PN->getParent() == LI->getHeader()) {
1929 // Okay, there is no closed form solution for the PHI node. Check
1930 // to see if the loop that contains it has a known iteration count.
1931 // If so, we may be able to force computation of the exit value.
1932 SCEVHandle IterationCount = getIterationCount(LI);
1933 if (SCEVConstant *ICC = dyn_cast<SCEVConstant>(IterationCount)) {
1934 // Okay, we know how many times the containing loop executes. If
1935 // this is a constant evolving PHI node, get the final value at
1936 // the specified iteration number.
1937 Constant *RV = getConstantEvolutionLoopExitValue(PN,
1938 ICC->getValue()->getZExtValue(),
1940 if (RV) return SCEVUnknown::get(RV);
1944 // Okay, this is a some expression that we cannot symbolically evaluate
1945 // into a SCEV. Check to see if it's possible to symbolically evaluate
1946 // the arguments into constants, and if see, try to constant propagate the
1947 // result. This is particularly useful for computing loop exit values.
1948 if (CanConstantFold(I)) {
1949 std::vector<Constant*> Operands;
1950 Operands.reserve(I->getNumOperands());
1951 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
1952 Value *Op = I->getOperand(i);
1953 if (Constant *C = dyn_cast<Constant>(Op)) {
1954 Operands.push_back(C);
1956 SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L);
1957 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV))
1958 Operands.push_back(ConstantExpr::getCast(SC->getValue(),
1960 else if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) {
1961 if (Constant *C = dyn_cast<Constant>(SU->getValue()))
1962 Operands.push_back(ConstantExpr::getCast(C, Op->getType()));
1970 return SCEVUnknown::get(ConstantFold(I, Operands));
1974 // This is some other type of SCEVUnknown, just return it.
1978 if (SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
1979 // Avoid performing the look-up in the common case where the specified
1980 // expression has no loop-variant portions.
1981 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
1982 SCEVHandle OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
1983 if (OpAtScope != Comm->getOperand(i)) {
1984 if (OpAtScope == UnknownValue) return UnknownValue;
1985 // Okay, at least one of these operands is loop variant but might be
1986 // foldable. Build a new instance of the folded commutative expression.
1987 std::vector<SCEVHandle> NewOps(Comm->op_begin(), Comm->op_begin()+i);
1988 NewOps.push_back(OpAtScope);
1990 for (++i; i != e; ++i) {
1991 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
1992 if (OpAtScope == UnknownValue) return UnknownValue;
1993 NewOps.push_back(OpAtScope);
1995 if (isa<SCEVAddExpr>(Comm))
1996 return SCEVAddExpr::get(NewOps);
1997 assert(isa<SCEVMulExpr>(Comm) && "Only know about add and mul!");
1998 return SCEVMulExpr::get(NewOps);
2001 // If we got here, all operands are loop invariant.
2005 if (SCEVSDivExpr *Div = dyn_cast<SCEVSDivExpr>(V)) {
2006 SCEVHandle LHS = getSCEVAtScope(Div->getLHS(), L);
2007 if (LHS == UnknownValue) return LHS;
2008 SCEVHandle RHS = getSCEVAtScope(Div->getRHS(), L);
2009 if (RHS == UnknownValue) return RHS;
2010 if (LHS == Div->getLHS() && RHS == Div->getRHS())
2011 return Div; // must be loop invariant
2012 return SCEVSDivExpr::get(LHS, RHS);
2015 // If this is a loop recurrence for a loop that does not contain L, then we
2016 // are dealing with the final value computed by the loop.
2017 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
2018 if (!L || !AddRec->getLoop()->contains(L->getHeader())) {
2019 // To evaluate this recurrence, we need to know how many times the AddRec
2020 // loop iterates. Compute this now.
2021 SCEVHandle IterationCount = getIterationCount(AddRec->getLoop());
2022 if (IterationCount == UnknownValue) return UnknownValue;
2023 IterationCount = getTruncateOrZeroExtend(IterationCount,
2026 // If the value is affine, simplify the expression evaluation to just
2027 // Start + Step*IterationCount.
2028 if (AddRec->isAffine())
2029 return SCEVAddExpr::get(AddRec->getStart(),
2030 SCEVMulExpr::get(IterationCount,
2031 AddRec->getOperand(1)));
2033 // Otherwise, evaluate it the hard way.
2034 return AddRec->evaluateAtIteration(IterationCount);
2036 return UnknownValue;
2039 //assert(0 && "Unknown SCEV type!");
2040 return UnknownValue;
2044 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
2045 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
2046 /// might be the same) or two SCEVCouldNotCompute objects.
2048 static std::pair<SCEVHandle,SCEVHandle>
2049 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec) {
2050 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
2051 SCEVConstant *L = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
2052 SCEVConstant *M = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
2053 SCEVConstant *N = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
2055 // We currently can only solve this if the coefficients are constants.
2056 if (!L || !M || !N) {
2057 SCEV *CNC = new SCEVCouldNotCompute();
2058 return std::make_pair(CNC, CNC);
2061 Constant *Two = ConstantInt::get(L->getValue()->getType(), 2);
2063 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
2064 Constant *C = L->getValue();
2065 // The B coefficient is M-N/2
2066 Constant *B = ConstantExpr::getSub(M->getValue(),
2067 ConstantExpr::getDiv(N->getValue(),
2069 // The A coefficient is N/2
2070 Constant *A = ConstantExpr::getDiv(N->getValue(), Two);
2072 // Compute the B^2-4ac term.
2073 Constant *SqrtTerm =
2074 ConstantExpr::getMul(ConstantInt::get(C->getType(), 4),
2075 ConstantExpr::getMul(A, C));
2076 SqrtTerm = ConstantExpr::getSub(ConstantExpr::getMul(B, B), SqrtTerm);
2078 // Compute floor(sqrt(B^2-4ac))
2079 ConstantInt *SqrtVal =
2080 cast<ConstantInt>(ConstantExpr::getCast(SqrtTerm,
2081 SqrtTerm->getType()->getUnsignedVersion()));
2082 uint64_t SqrtValV = SqrtVal->getZExtValue();
2083 uint64_t SqrtValV2 = (uint64_t)sqrt((double)SqrtValV);
2084 // The square root might not be precise for arbitrary 64-bit integer
2085 // values. Do some sanity checks to ensure it's correct.
2086 if (SqrtValV2*SqrtValV2 > SqrtValV ||
2087 (SqrtValV2+1)*(SqrtValV2+1) <= SqrtValV) {
2088 SCEV *CNC = new SCEVCouldNotCompute();
2089 return std::make_pair(CNC, CNC);
2092 SqrtVal = ConstantInt::get(Type::ULongTy, SqrtValV2);
2093 SqrtTerm = ConstantExpr::getCast(SqrtVal, SqrtTerm->getType());
2095 Constant *NegB = ConstantExpr::getNeg(B);
2096 Constant *TwoA = ConstantExpr::getMul(A, Two);
2098 // The divisions must be performed as signed divisions.
2099 const Type *SignedTy = NegB->getType()->getSignedVersion();
2100 NegB = ConstantExpr::getCast(NegB, SignedTy);
2101 TwoA = ConstantExpr::getCast(TwoA, SignedTy);
2102 SqrtTerm = ConstantExpr::getCast(SqrtTerm, SignedTy);
2104 Constant *Solution1 =
2105 ConstantExpr::getDiv(ConstantExpr::getAdd(NegB, SqrtTerm), TwoA);
2106 Constant *Solution2 =
2107 ConstantExpr::getDiv(ConstantExpr::getSub(NegB, SqrtTerm), TwoA);
2108 return std::make_pair(SCEVUnknown::get(Solution1),
2109 SCEVUnknown::get(Solution2));
2112 /// HowFarToZero - Return the number of times a backedge comparing the specified
2113 /// value to zero will execute. If not computable, return UnknownValue
2114 SCEVHandle ScalarEvolutionsImpl::HowFarToZero(SCEV *V, const Loop *L) {
2115 // If the value is a constant
2116 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
2117 // If the value is already zero, the branch will execute zero times.
2118 if (C->getValue()->isNullValue()) return C;
2119 return UnknownValue; // Otherwise it will loop infinitely.
2122 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
2123 if (!AddRec || AddRec->getLoop() != L)
2124 return UnknownValue;
2126 if (AddRec->isAffine()) {
2127 // If this is an affine expression the execution count of this branch is
2130 // (0 - Start/Step) iff Start % Step == 0
2132 // Get the initial value for the loop.
2133 SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
2134 if (isa<SCEVCouldNotCompute>(Start)) return UnknownValue;
2135 SCEVHandle Step = AddRec->getOperand(1);
2137 Step = getSCEVAtScope(Step, L->getParentLoop());
2139 // Figure out if Start % Step == 0.
2140 // FIXME: We should add DivExpr and RemExpr operations to our AST.
2141 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) {
2142 if (StepC->getValue()->equalsInt(1)) // N % 1 == 0
2143 return SCEV::getNegativeSCEV(Start); // 0 - Start/1 == -Start
2144 if (StepC->getValue()->isAllOnesValue()) // N % -1 == 0
2145 return Start; // 0 - Start/-1 == Start
2147 // Check to see if Start is divisible by SC with no remainder.
2148 if (SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) {
2149 ConstantInt *StartCC = StartC->getValue();
2150 Constant *StartNegC = ConstantExpr::getNeg(StartCC);
2151 Constant *Rem = ConstantExpr::getRem(StartNegC, StepC->getValue());
2152 if (Rem->isNullValue()) {
2153 Constant *Result =ConstantExpr::getDiv(StartNegC,StepC->getValue());
2154 return SCEVUnknown::get(Result);
2158 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) {
2159 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
2160 // the quadratic equation to solve it.
2161 std::pair<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec);
2162 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
2163 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
2166 std::cerr << "HFTZ: " << *V << " - sol#1: " << *R1
2167 << " sol#2: " << *R2 << "\n";
2169 // Pick the smallest positive root value.
2170 assert(R1->getType()->isUnsigned()&&"Didn't canonicalize to unsigned?");
2171 if (ConstantBool *CB =
2172 dyn_cast<ConstantBool>(ConstantExpr::getSetLT(R1->getValue(),
2174 if (CB->getValue() == false)
2175 std::swap(R1, R2); // R1 is the minimum root now.
2177 // We can only use this value if the chrec ends up with an exact zero
2178 // value at this index. When solving for "X*X != 5", for example, we
2179 // should not accept a root of 2.
2180 SCEVHandle Val = AddRec->evaluateAtIteration(R1);
2181 if (SCEVConstant *EvalVal = dyn_cast<SCEVConstant>(Val))
2182 if (EvalVal->getValue()->isNullValue())
2183 return R1; // We found a quadratic root!
2188 return UnknownValue;
2191 /// HowFarToNonZero - Return the number of times a backedge checking the
2192 /// specified value for nonzero will execute. If not computable, return
2194 SCEVHandle ScalarEvolutionsImpl::HowFarToNonZero(SCEV *V, const Loop *L) {
2195 // Loops that look like: while (X == 0) are very strange indeed. We don't
2196 // handle them yet except for the trivial case. This could be expanded in the
2197 // future as needed.
2199 // If the value is a constant, check to see if it is known to be non-zero
2200 // already. If so, the backedge will execute zero times.
2201 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
2202 Constant *Zero = Constant::getNullValue(C->getValue()->getType());
2203 Constant *NonZero = ConstantExpr::getSetNE(C->getValue(), Zero);
2204 if (NonZero == ConstantBool::getTrue())
2205 return getSCEV(Zero);
2206 return UnknownValue; // Otherwise it will loop infinitely.
2209 // We could implement others, but I really doubt anyone writes loops like
2210 // this, and if they did, they would already be constant folded.
2211 return UnknownValue;
2214 /// HowManyLessThans - Return the number of times a backedge containing the
2215 /// specified less-than comparison will execute. If not computable, return
2217 SCEVHandle ScalarEvolutionsImpl::
2218 HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L) {
2219 // Only handle: "ADDREC < LoopInvariant".
2220 if (!RHS->isLoopInvariant(L)) return UnknownValue;
2222 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
2223 if (!AddRec || AddRec->getLoop() != L)
2224 return UnknownValue;
2226 if (AddRec->isAffine()) {
2227 // FORNOW: We only support unit strides.
2228 SCEVHandle One = SCEVUnknown::getIntegerSCEV(1, RHS->getType());
2229 if (AddRec->getOperand(1) != One)
2230 return UnknownValue;
2232 // The number of iterations for "[n,+,1] < m", is m-n. However, we don't
2233 // know that m is >= n on input to the loop. If it is, the condition return
2234 // true zero times. What we really should return, for full generality, is
2235 // SMAX(0, m-n). Since we cannot check this, we will instead check for a
2236 // canonical loop form: most do-loops will have a check that dominates the
2237 // loop, that only enters the loop if [n-1]<m. If we can find this check,
2238 // we know that the SMAX will evaluate to m-n, because we know that m >= n.
2240 // Search for the check.
2241 BasicBlock *Preheader = L->getLoopPreheader();
2242 BasicBlock *PreheaderDest = L->getHeader();
2243 if (Preheader == 0) return UnknownValue;
2245 BranchInst *LoopEntryPredicate =
2246 dyn_cast<BranchInst>(Preheader->getTerminator());
2247 if (!LoopEntryPredicate) return UnknownValue;
2249 // This might be a critical edge broken out. If the loop preheader ends in
2250 // an unconditional branch to the loop, check to see if the preheader has a
2251 // single predecessor, and if so, look for its terminator.
2252 while (LoopEntryPredicate->isUnconditional()) {
2253 PreheaderDest = Preheader;
2254 Preheader = Preheader->getSinglePredecessor();
2255 if (!Preheader) return UnknownValue; // Multiple preds.
2257 LoopEntryPredicate =
2258 dyn_cast<BranchInst>(Preheader->getTerminator());
2259 if (!LoopEntryPredicate) return UnknownValue;
2262 // Now that we found a conditional branch that dominates the loop, check to
2263 // see if it is the comparison we are looking for.
2264 SetCondInst *SCI =dyn_cast<SetCondInst>(LoopEntryPredicate->getCondition());
2265 if (!SCI) return UnknownValue;
2266 Value *PreCondLHS = SCI->getOperand(0);
2267 Value *PreCondRHS = SCI->getOperand(1);
2268 Instruction::BinaryOps Cond;
2269 if (LoopEntryPredicate->getSuccessor(0) == PreheaderDest)
2270 Cond = SCI->getOpcode();
2272 Cond = SCI->getInverseCondition();
2275 case Instruction::SetGT:
2276 std::swap(PreCondLHS, PreCondRHS);
2277 Cond = Instruction::SetLT;
2279 case Instruction::SetLT:
2280 if (PreCondLHS->getType()->isInteger() &&
2281 PreCondLHS->getType()->isSigned()) {
2282 if (RHS != getSCEV(PreCondRHS))
2283 return UnknownValue; // Not a comparison against 'm'.
2285 if (SCEV::getMinusSCEV(AddRec->getOperand(0), One)
2286 != getSCEV(PreCondLHS))
2287 return UnknownValue; // Not a comparison against 'n-1'.
2290 return UnknownValue;
2295 //std::cerr << "Computed Loop Trip Count as: " <<
2296 // *SCEV::getMinusSCEV(RHS, AddRec->getOperand(0)) << "\n";
2297 return SCEV::getMinusSCEV(RHS, AddRec->getOperand(0));
2300 return UnknownValue;
2303 /// getNumIterationsInRange - Return the number of iterations of this loop that
2304 /// produce values in the specified constant range. Another way of looking at
2305 /// this is that it returns the first iteration number where the value is not in
2306 /// the condition, thus computing the exit count. If the iteration count can't
2307 /// be computed, an instance of SCEVCouldNotCompute is returned.
2308 SCEVHandle SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range) const {
2309 if (Range.isFullSet()) // Infinite loop.
2310 return new SCEVCouldNotCompute();
2312 // If the start is a non-zero constant, shift the range to simplify things.
2313 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
2314 if (!SC->getValue()->isNullValue()) {
2315 std::vector<SCEVHandle> Operands(op_begin(), op_end());
2316 Operands[0] = SCEVUnknown::getIntegerSCEV(0, SC->getType());
2317 SCEVHandle Shifted = SCEVAddRecExpr::get(Operands, getLoop());
2318 if (SCEVAddRecExpr *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted))
2319 return ShiftedAddRec->getNumIterationsInRange(
2320 Range.subtract(SC->getValue()));
2321 // This is strange and shouldn't happen.
2322 return new SCEVCouldNotCompute();
2325 // The only time we can solve this is when we have all constant indices.
2326 // Otherwise, we cannot determine the overflow conditions.
2327 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
2328 if (!isa<SCEVConstant>(getOperand(i)))
2329 return new SCEVCouldNotCompute();
2332 // Okay at this point we know that all elements of the chrec are constants and
2333 // that the start element is zero.
2335 // First check to see if the range contains zero. If not, the first
2337 ConstantInt *Zero = ConstantInt::get(getType(), 0);
2338 if (!Range.contains(Zero)) return SCEVConstant::get(Zero);
2341 // If this is an affine expression then we have this situation:
2342 // Solve {0,+,A} in Range === Ax in Range
2344 // Since we know that zero is in the range, we know that the upper value of
2345 // the range must be the first possible exit value. Also note that we
2346 // already checked for a full range.
2347 ConstantInt *Upper = cast<ConstantInt>(Range.getUpper());
2348 ConstantInt *A = cast<SCEVConstant>(getOperand(1))->getValue();
2349 ConstantInt *One = ConstantInt::get(getType(), 1);
2351 // The exit value should be (Upper+A-1)/A.
2352 Constant *ExitValue = Upper;
2354 ExitValue = ConstantExpr::getSub(ConstantExpr::getAdd(Upper, A), One);
2355 ExitValue = ConstantExpr::getDiv(ExitValue, A);
2357 assert(isa<ConstantInt>(ExitValue) &&
2358 "Constant folding of integers not implemented?");
2360 // Evaluate at the exit value. If we really did fall out of the valid
2361 // range, then we computed our trip count, otherwise wrap around or other
2362 // things must have happened.
2363 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue);
2364 if (Range.contains(Val))
2365 return new SCEVCouldNotCompute(); // Something strange happened
2367 // Ensure that the previous value is in the range. This is a sanity check.
2368 assert(Range.contains(EvaluateConstantChrecAtConstant(this,
2369 ConstantExpr::getSub(ExitValue, One))) &&
2370 "Linear scev computation is off in a bad way!");
2371 return SCEVConstant::get(cast<ConstantInt>(ExitValue));
2372 } else if (isQuadratic()) {
2373 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
2374 // quadratic equation to solve it. To do this, we must frame our problem in
2375 // terms of figuring out when zero is crossed, instead of when
2376 // Range.getUpper() is crossed.
2377 std::vector<SCEVHandle> NewOps(op_begin(), op_end());
2378 NewOps[0] = SCEV::getNegativeSCEV(SCEVUnknown::get(Range.getUpper()));
2379 SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewOps, getLoop());
2381 // Next, solve the constructed addrec
2382 std::pair<SCEVHandle,SCEVHandle> Roots =
2383 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec));
2384 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
2385 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
2387 // Pick the smallest positive root value.
2388 assert(R1->getType()->isUnsigned() && "Didn't canonicalize to unsigned?");
2389 if (ConstantBool *CB =
2390 dyn_cast<ConstantBool>(ConstantExpr::getSetLT(R1->getValue(),
2392 if (CB->getValue() == false)
2393 std::swap(R1, R2); // R1 is the minimum root now.
2395 // Make sure the root is not off by one. The returned iteration should
2396 // not be in the range, but the previous one should be. When solving
2397 // for "X*X < 5", for example, we should not return a root of 2.
2398 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
2400 if (Range.contains(R1Val)) {
2401 // The next iteration must be out of the range...
2403 ConstantExpr::getAdd(R1->getValue(),
2404 ConstantInt::get(R1->getType(), 1));
2406 R1Val = EvaluateConstantChrecAtConstant(this, NextVal);
2407 if (!Range.contains(R1Val))
2408 return SCEVUnknown::get(NextVal);
2409 return new SCEVCouldNotCompute(); // Something strange happened
2412 // If R1 was not in the range, then it is a good return value. Make
2413 // sure that R1-1 WAS in the range though, just in case.
2415 ConstantExpr::getSub(R1->getValue(),
2416 ConstantInt::get(R1->getType(), 1));
2417 R1Val = EvaluateConstantChrecAtConstant(this, NextVal);
2418 if (Range.contains(R1Val))
2420 return new SCEVCouldNotCompute(); // Something strange happened
2425 // Fallback, if this is a general polynomial, figure out the progression
2426 // through brute force: evaluate until we find an iteration that fails the
2427 // test. This is likely to be slow, but getting an accurate trip count is
2428 // incredibly important, we will be able to simplify the exit test a lot, and
2429 // we are almost guaranteed to get a trip count in this case.
2430 ConstantInt *TestVal = ConstantInt::get(getType(), 0);
2431 ConstantInt *One = ConstantInt::get(getType(), 1);
2432 ConstantInt *EndVal = TestVal; // Stop when we wrap around.
2434 ++NumBruteForceEvaluations;
2435 SCEVHandle Val = evaluateAtIteration(SCEVConstant::get(TestVal));
2436 if (!isa<SCEVConstant>(Val)) // This shouldn't happen.
2437 return new SCEVCouldNotCompute();
2439 // Check to see if we found the value!
2440 if (!Range.contains(cast<SCEVConstant>(Val)->getValue()))
2441 return SCEVConstant::get(TestVal);
2443 // Increment to test the next index.
2444 TestVal = cast<ConstantInt>(ConstantExpr::getAdd(TestVal, One));
2445 } while (TestVal != EndVal);
2447 return new SCEVCouldNotCompute();
2452 //===----------------------------------------------------------------------===//
2453 // ScalarEvolution Class Implementation
2454 //===----------------------------------------------------------------------===//
2456 bool ScalarEvolution::runOnFunction(Function &F) {
2457 Impl = new ScalarEvolutionsImpl(F, getAnalysis<LoopInfo>());
2461 void ScalarEvolution::releaseMemory() {
2462 delete (ScalarEvolutionsImpl*)Impl;
2466 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
2467 AU.setPreservesAll();
2468 AU.addRequiredTransitive<LoopInfo>();
2471 SCEVHandle ScalarEvolution::getSCEV(Value *V) const {
2472 return ((ScalarEvolutionsImpl*)Impl)->getSCEV(V);
2475 /// hasSCEV - Return true if the SCEV for this value has already been
2477 bool ScalarEvolution::hasSCEV(Value *V) const {
2478 return ((ScalarEvolutionsImpl*)Impl)->hasSCEV(V);
2482 /// setSCEV - Insert the specified SCEV into the map of current SCEVs for
2483 /// the specified value.
2484 void ScalarEvolution::setSCEV(Value *V, const SCEVHandle &H) {
2485 ((ScalarEvolutionsImpl*)Impl)->setSCEV(V, H);
2489 SCEVHandle ScalarEvolution::getIterationCount(const Loop *L) const {
2490 return ((ScalarEvolutionsImpl*)Impl)->getIterationCount(L);
2493 bool ScalarEvolution::hasLoopInvariantIterationCount(const Loop *L) const {
2494 return !isa<SCEVCouldNotCompute>(getIterationCount(L));
2497 SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) const {
2498 return ((ScalarEvolutionsImpl*)Impl)->getSCEVAtScope(getSCEV(V), L);
2501 void ScalarEvolution::deleteInstructionFromRecords(Instruction *I) const {
2502 return ((ScalarEvolutionsImpl*)Impl)->deleteInstructionFromRecords(I);
2505 static void PrintLoopInfo(std::ostream &OS, const ScalarEvolution *SE,
2507 // Print all inner loops first
2508 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
2509 PrintLoopInfo(OS, SE, *I);
2511 std::cerr << "Loop " << L->getHeader()->getName() << ": ";
2513 std::vector<BasicBlock*> ExitBlocks;
2514 L->getExitBlocks(ExitBlocks);
2515 if (ExitBlocks.size() != 1)
2516 std::cerr << "<multiple exits> ";
2518 if (SE->hasLoopInvariantIterationCount(L)) {
2519 std::cerr << *SE->getIterationCount(L) << " iterations! ";
2521 std::cerr << "Unpredictable iteration count. ";
2527 void ScalarEvolution::print(std::ostream &OS, const Module* ) const {
2528 Function &F = ((ScalarEvolutionsImpl*)Impl)->F;
2529 LoopInfo &LI = ((ScalarEvolutionsImpl*)Impl)->LI;
2531 OS << "Classifying expressions for: " << F.getName() << "\n";
2532 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
2533 if (I->getType()->isInteger()) {
2536 SCEVHandle SV = getSCEV(&*I);
2540 if ((*I).getType()->isIntegral()) {
2541 ConstantRange Bounds = SV->getValueRange();
2542 if (!Bounds.isFullSet())
2543 OS << "Bounds: " << Bounds << " ";
2546 if (const Loop *L = LI.getLoopFor((*I).getParent())) {
2548 SCEVHandle ExitValue = getSCEVAtScope(&*I, L->getParentLoop());
2549 if (isa<SCEVCouldNotCompute>(ExitValue)) {
2550 OS << "<<Unknown>>";
2560 OS << "Determining loop execution counts for: " << F.getName() << "\n";
2561 for (LoopInfo::iterator I = LI.begin(), E = LI.end(); I != E; ++I)
2562 PrintLoopInfo(OS, this, *I);